TSTP Solution File: ALG428-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG428-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:32:42 EDT 2023
% Result : Unsatisfiable 29.38s 13.53s
% Output : CNFRefutation 29.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 77
% Syntax : Number of formulae : 90 ( 11 unt; 70 typ; 0 def)
% Number of atoms : 36 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 66 >; 24 *; 0 +; 0 <<)
% Number of predicates : 55 ( 53 usr; 2 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 16 (; 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > c_Parity_Oeven__odd__class_Oeven > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring__0 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Ocomm__ring__1 > class_Ring__and__Field_Ocomm__ring > class_RealVector_Oreal__normed__algebra > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oordered__ab__group__add > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__comm__monoid__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > class_HOL_Ozero > class_Divides_Osemiring__div > class_Divides_Oring__div > c_Polynomial_OpCons > c_Orderings_Oord__class_Omin > c_Orderings_Oord__class_Omax > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly > c_Divides_Odiv__class_Omod > c_Polynomial_Odegree > c_HOL_Ouminus__class_Ouminus > c_Fundamental__Theorem__Algebra__Mirabelle_Opsize > #nlpp > tc_Polynomial_Opoly > c_Suc > c_HOL_Ozero__class_Ozero > v_thesis____ > v_p > tc_nat > tc_Complex_Ocomplex
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_HOL_Ozero,type,
class_HOL_Ozero: $i > $o ).
tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(class_OrderedGroup_Ocancel__comm__monoid__add,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__0,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(class_OrderedGroup_Oordered__ab__group__add,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Parity_Oeven__odd__class_Oeven,type,
c_Parity_Oeven__odd__class_Oeven: ( $i * $i ) > $o ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(tc_Polynomial_Opoly,type,
tc_Polynomial_Opoly: $i > $i ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(v_thesis____,type,
v_thesis____: $o ).
tff(class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(c_Orderings_Oord__class_Omin,type,
c_Orderings_Oord__class_Omin: ( $i * $i * $i ) > $i ).
tff(c_Suc,type,
c_Suc: $i > $i ).
tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(class_Ring__and__Field_Ocomm__ring__1,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_Divides_Oring__div,type,
class_Divides_Oring__div: $i > $o ).
tff(class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_nat,type,
tc_nat: $i ).
tff(c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(c_Orderings_Oord__class_Omax,type,
c_Orderings_Oord__class_Omax: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(class_Ring__and__Field_Ocomm__ring,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Polynomial_OpCons,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Omult__mono1,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(c_HOL_Ouminus__class_Ouminus,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(c_Polynomial_Odegree,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
tff(class_Ring__and__Field_Omult__mono,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(v_p,type,
v_p: $i ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(f_2300,axiom,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file(unknown,unknown) ).
tff(f_5335,axiom,
class_Orderings_Olinorder(tc_nat),
file(unknown,unknown) ).
tff(f_231,axiom,
! [T_a,V_y,V_x] :
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ( V_x = V_y ) ),
file(unknown,unknown) ).
tff(f_592,axiom,
! [V_n] :
( ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
file(unknown,unknown) ).
tff(f_5283,axiom,
~ v_thesis____,
file(unknown,unknown) ).
tff(f_5288,axiom,
! [V_x] :
( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(V_x) )
| v_thesis____ ),
file(unknown,unknown) ).
tff(f_5281,axiom,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
file(unknown,unknown) ).
tff(c_640,plain,
! [V_n_960] : ~ c_HOL_Oord__class_Oless(V_n_960,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnfTransformation,[status(thm)],[f_2300]) ).
tff(c_1656,plain,
class_Orderings_Olinorder(tc_nat),
inference(cnfTransformation,[status(thm)],[f_5335]) ).
tff(c_58,plain,
! [V_y_87,V_x_88,T_a_86] :
( ( V_y_87 = V_x_88 )
| c_HOL_Oord__class_Oless(V_x_88,V_y_87,T_a_86)
| c_HOL_Oord__class_Oless(V_y_87,V_x_88,T_a_86)
| ~ class_Orderings_Olinorder(T_a_86) ),
inference(cnfTransformation,[status(thm)],[f_231]) ).
tff(c_50025,plain,
! [V_n_3403] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n_3403,tc_nat)
| ( c_Suc(c_HOL_Ominus__class_Ominus(V_n_3403,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n_3403 ) ),
inference(cnfTransformation,[status(thm)],[f_592]) ).
tff(c_1584,plain,
~ v_thesis____,
inference(cnfTransformation,[status(thm)],[f_5283]) ).
tff(c_1586,plain,
! [V_x_2292] :
( v_thesis____
| ( c_Suc(V_x_2292) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ) ),
inference(cnfTransformation,[status(thm)],[f_5288]) ).
tff(c_1783,plain,
! [V_x_2292] : ( c_Suc(V_x_2292) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ),
inference(negUnitSimplification,[status(thm)],[c_1584,c_1586]) ).
tff(c_74850,plain,
! [V_n_3668] :
( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != V_n_3668 )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n_3668,tc_nat) ),
inference(superposition,[status(thm),theory(equality)],[c_50025,c_1783]) ).
tff(c_74913,plain,
! [V_y_87] :
( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != V_y_87 )
| ( c_HOL_Ozero__class_Ozero(tc_nat) = V_y_87 )
| c_HOL_Oord__class_Oless(V_y_87,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[c_58,c_74850]) ).
tff(c_75021,plain,
! [V_y_87] :
( ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != V_y_87 )
| ( c_HOL_Ozero__class_Ozero(tc_nat) = V_y_87 )
| c_HOL_Oord__class_Oless(V_y_87,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(demodulation,[status(thm),theory(equality)],[c_1656,c_74913]) ).
tff(c_75057,plain,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(negUnitSimplification,[status(thm)],[c_640,c_75021]) ).
tff(c_1582,plain,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnfTransformation,[status(thm)],[f_5281]) ).
tff(c_75062,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_75057,c_1582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG428-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Aug 3 20:18:51 EDT 2023
% 0.12/0.32 % CPUTime :
% 29.38/13.53 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.38/13.53
% 29.38/13.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.54/13.56
% 29.54/13.56 Inference rules
% 29.54/13.56 ----------------------
% 29.54/13.56 #Ref : 34
% 29.54/13.56 #Sup : 16023
% 29.54/13.56 #Fact : 10
% 29.54/13.56 #Define : 0
% 29.54/13.56 #Split : 7
% 29.54/13.56 #Chain : 0
% 29.54/13.56 #Close : 0
% 29.54/13.56
% 29.54/13.56 Ordering : KBO
% 29.54/13.56
% 29.54/13.56 Simplification rules
% 29.54/13.56 ----------------------
% 29.54/13.56 #Subsume : 5389
% 29.54/13.56 #Demod : 8737
% 29.54/13.56 #Tautology : 4723
% 29.54/13.56 #SimpNegUnit : 396
% 29.54/13.56 #BackRed : 12
% 29.54/13.56
% 29.54/13.56 #Partial instantiations: 0
% 29.54/13.56 #Strategies tried : 1
% 29.54/13.56
% 29.54/13.56 Timing (in seconds)
% 29.54/13.56 ----------------------
% 29.54/13.57 Preprocessing : 1.60
% 29.54/13.57 Parsing : 0.91
% 29.54/13.57 CNF conversion : 0.13
% 29.54/13.57 Main loop : 10.91
% 29.54/13.57 Inferencing : 1.70
% 29.54/13.57 Reduction : 5.50
% 29.54/13.57 Demodulation : 4.08
% 29.54/13.57 BG Simplification : 0.22
% 29.54/13.57 Subsumption : 2.89
% 29.54/13.57 Abstraction : 0.17
% 29.54/13.57 MUC search : 0.00
% 29.54/13.57 Cooper : 0.00
% 29.54/13.57 Total : 12.56
% 29.54/13.57 Index Insertion : 0.00
% 29.54/13.57 Index Deletion : 0.00
% 29.54/13.57 Index Matching : 0.00
% 29.54/13.57 BG Taut test : 0.00
%------------------------------------------------------------------------------